Modelling soil pollution in the Nederlands
## Loading required package: nlme
## Warning: package 'nlme' was built under R version 3.6.2
## This is mgcv 1.8-31. For overview type 'help("mgcv-package")'.
## 'data.frame': 155 obs. of 14 variables:
## $ x : num 181072 181025 181165 181298 181307 ...
## $ y : num 333611 333558 333537 333484 333330 ...
## $ cadmium: num 11.7 8.6 6.5 2.6 2.8 3 3.2 2.8 2.4 1.6 ...
## $ copper : num 85 81 68 81 48 61 31 29 37 24 ...
## $ lead : num 299 277 199 116 117 137 132 150 133 80 ...
## $ zinc : num 1022 1141 640 257 269 ...
## $ elev : num 7.91 6.98 7.8 7.66 7.48 ...
## $ dist : num 0.00136 0.01222 0.10303 0.19009 0.27709 ...
## $ om : num 13.6 14 13 8 8.7 7.8 9.2 9.5 10.6 6.3 ...
## $ ffreq : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ soil : Factor w/ 3 levels "1","2","3": 1 1 1 2 2 2 2 1 1 2 ...
## $ lime : Factor w/ 2 levels "0","1": 2 2 2 1 1 1 1 1 1 1 ...
## $ landuse: Factor w/ 15 levels "Aa","Ab","Ag",..: 4 4 4 11 4 11 4 2 2 15 ...
## $ dist.m : num 50 30 150 270 380 470 240 120 240 420 ...
##
## Family: gaussian
## Link function: identity
##
## Formula:
## cadmium ~ s(x, y)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.2458 0.1774 18.3 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(x,y) 23.48 27.24 8.667 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.607 Deviance explained = 66.7%
## -REML = 372.07 Scale est. = 4.8757 n = 155
## (Intercept) s(x,y).1 s(x,y).2 s(x,y).3 s(x,y).4 s(x,y).5
## 3.2458065 0.8686658 -10.2154908 6.4161781 -2.6784725 9.1807111
## s(x,y).6 s(x,y).7 s(x,y).8 s(x,y).9 s(x,y).10 s(x,y).11
## 3.7004932 -10.4780937 -8.9821840 -0.6218677 -4.6789789 -5.4267313
## s(x,y).12 s(x,y).13 s(x,y).14 s(x,y).15 s(x,y).16 s(x,y).17
## 7.4996452 8.1962843 -7.6311640 4.5829340 -0.9734724 0.7634059
## s(x,y).18 s(x,y).19 s(x,y).20 s(x,y).21 s(x,y).22 s(x,y).23
## 8.8112827 -4.8639552 -6.8085148 3.8059356 6.3499868 6.4701169
## s(x,y).24 s(x,y).25 s(x,y).26 s(x,y).27 s(x,y).28 s(x,y).29
## -8.1556061 7.2050985 0.1567317 -53.4384704 -4.2860149 5.5212533
Soil pollution in different land uses
##
## Family: gaussian
## Link function: identity
##
## Formula:
## copper ~ s(dist, by = landuse) + landuse
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.115 46.336 0.434 0.665
## landuseAb 15.674 46.608 0.336 0.737
## landuseAg 6.670 46.825 0.142 0.887
## landuseAh 18.137 46.396 0.391 0.697
## landuseAm 13.364 46.439 0.288 0.774
## landuseB 0.825 62.980 0.013 0.990
## landuseBw 18.909 46.756 0.404 0.687
## landuseDEN 0.000 0.000 NA NA
## landuseFh 4.885 155.441 0.031 0.975
## landuseFw 18.578 46.572 0.399 0.691
## landuseGa 122.541 99.225 1.235 0.219
## landuseSPO 1.885 146.521 0.013 0.990
## landuseSTA 3.261 49.282 0.066 0.947
## landuseTv 4.885 134.312 0.036 0.971
## landuseW 18.917 46.442 0.407 0.684
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(dist):landuseAa 1.000e+00 1.000e+00 0.000 0.98367
## s(dist):landuseAb 1.000e+00 1.000e+00 1.672 0.19842
## s(dist):landuseAg 1.000e+00 1.000e+00 0.442 0.50767
## s(dist):landuseAh 2.524e+00 3.113e+00 8.725 2.11e-05 ***
## s(dist):landuseAm 1.000e+00 1.000e+00 6.802 0.01022 *
## s(dist):landuseB 1.000e+00 1.000e+00 0.023 0.87889
## s(dist):landuseBw 1.000e+00 1.000e+00 0.047 0.82886
## s(dist):landuseDEN 1.000e+00 1.000e+00 0.042 0.83865
## s(dist):landuseFh -6.730e-16 -6.730e-16 0.000 1.00000
## s(dist):landuseFw 2.696e+00 3.304e+00 5.292 0.00131 **
## s(dist):landuseGa 1.882e+00 1.986e+00 0.654 0.49474
## s(dist):landuseSPO -3.189e-16 -3.189e-16 0.000 1.00000
## s(dist):landuseSTA 1.000e+00 1.000e+00 0.005 0.94455
## s(dist):landuseTv -1.713e-15 -1.713e-15 0.000 1.00000
## s(dist):landuseW 4.009e+00 4.814e+00 32.861 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 146/150
## R-sq.(adj) = 0.634 Deviance explained = 71.1%
## -REML = 532.81 Scale est. = 199.48 n = 154
##
## Family: gaussian
## Link function: identity
##
## Formula:
## copper ~ s(dist, landuse, bs = "fs")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.07 3.33 9.031 1.43e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(dist,landuse) 16.37 71 2.463 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.533 Deviance explained = 58.3%
## -REML = 659.94 Scale est. = 254.2 n = 154
Polution models with multi-scale interactions
##
## Family: gaussian
## Link function: identity
##
## Formula:
## cadmium ~ te(x, y, elev)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.2458 0.1329 24.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## te(x,y,elev) 38.29 45.86 11.87 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.78 Deviance explained = 83.4%
## -REML = 318.09 Scale est. = 2.7358 n = 155

##
## Family: gaussian
## Link function: identity
##
## Formula:
## cadmium ~ s(x, y) + s(elev) + ti(x, y, elev)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.7044 0.2244 12.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(x,y) 21.812 25.491 6.386 7.29e-15 ***
## s(elev) 3.898 4.688 9.680 1.98e-07 ***
## ti(x,y,elev) 14.656 19.180 2.706 0.000516 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.793 Deviance explained = 84.7%
## -REML = 336.62 Scale est. = 2.5755 n = 155
